Arturo Magidin

Dominions in varieties of nilpotent groups

We investigate the concept of dominion (in the sense of Isbell) in several varieties of nilpotent groups. We obtain a complete description of dominions in the variety of nilpotent groups of class at most two. Then we look at the behavior of dominions of subgroups of groups in N 2 when taken in the context of Nc for c>2. Finally, we establish the existence of nontrivial dominions in the category of all nilpotent groups.

Capability of nilpotent products of cyclic groups

Abstract A group is called capable if it is a central factor group. We consider the capability of nilpotent products of cyclic groups, and obtain a generalization of a theorem of Baer for the small class case. The approach is also used to obtain some recent results on the capability of certain nilpo tent groups of class 2. We also establish a necessary condition for the capability of an arbitrary p -group of class k, and some further results.

Computational Group Theory and the Theory of Groups

On the application of computational group theory to the theory of groups by R. F. Morse A classification of certain maximal subgroups of alternating groups by B. Benesh On the nonabelian tensor squares of free nilpotent groups of finite rank by R. D. Blyth, P. Moravec, and R. F. Morse Investigating

Capable 2-Generator 2-Groups of Class Two

p

Two generator p-groups of nilpotency class 2 and their conjugacy classes

-groups by coclass with GAP by H. Dietrich, B. Eick, and D. Feichtenschlager Homological algebra programming by G. Ellis Groups with a finite covering by siomorphic abelian subgroups by T. S. Foguel and M. F. Ragland On some subnormality conditions in metabelian groups by D. Garrison and L.-C. Kappe Normalizer calculation using automorphisms by A. Hulpke Group theory in SAGE by D. Joyner and D. Kohel Simultaneous constructions of the sporadic groups

Dominions in varieties generated by simple groups

\mathsf{Co_2}

Dominions in finitely generated nilpotent groups

and

Gauss's Lemma for Number Fields

\mathsf{Fi_{22}}

On the capability of finite groups of class two and prime exponent

by H. K. Kim and G. O. Michler Constructing simple groups from irreducible subgroups of

EMBEDDING GROUPS OF CLASS TWO AND PRIME EXPONENT IN CAPABLE AND NONCAPABLE GROUPS

GL_n(2)